Real Madrid have submitted a second, improved offer of €180 million to Paris Saint-Germain for Kylian Mbappe, sources have told ESPN.

An initial €160m bid was rejected on Tuesday, and sources close to Madrid have told ESPN the signing would be difficult, but they were hopeful of completing the deal before the transfer window closes on Aug. 31.

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The second offer of €180m consists of a flat €170m with a possible €10m in add-ons which sources told ESPN are "easily achievable."

PSG are yet to respond to the second offer but sources in Paris have told ESPN it is likely to be turned down as they are holding out for nearer €220m.

Mbappe has a year left on his contract and has already rejected several renewal offers, leaving the Ligue 1 club in the difficult position of risking losing him for nothing next summer.

Madrid would be able to negotiate with the France forward from January 2021 with a view to signing him for free when his PSG contract expires next June.

Mbappe has been a long-term, first-choice target for Real Madrid as president Florentino Perez -- who is personally overseeing the negotiations -- looks to build a new team to shine at the redeveloped Bernabeu stadium.

The club has known for months that the 22-year-old was keen to join, and ESPN reported in September that careful preparations were being made to make a move for Mbappe this summer.

However, at the same time, Madrid have been desperate not to act in a way that could anger PSG and threaten a possible deal, as well as the relationship between the two clubs.

Over the last week, sources told ESPN that there was a growing optimism at the Bernabeu about the club's chances of pulling off the signing.

Madrid have brought in around €80m from the sales of Raphael Varane to Manchester United and Martin Odegaard to Arsenal this summer and have not paid a transfer fee for a first team player since 2019, choosing instead to save up for when the moment came to bid for Mbappe.